Question: Find the general solution of
$$x^2 (y-xy') =y(y') ^2$$
if the singular solution doesn't exist.
Now, I know that it has to be solved by Clairaut's equation.
However, the given equation is not of the form $y=px+f(p)$ where $p=y'$ and cannot, as far as I know, be reduced to this form.
I even tried arranging the equation in the form of a quadratic in $y'$ but when I find the solution it yields a rather big equation that doesn't really lead anywhere.
Please let me know if you have any suggestions.